The Sky Blues, playing all in black, took the lead after 19 minutes when Jordan Henderson's deflected shot beat David Marshall.
Although the Canaries came back strongly and drew level thanks to Jonathan Grounds' snap-shot, they were undone by a bit of magic from Daniel Fox.
Coventry kicked off attacking the River End goal and went close to scoring in the seventh minute when Aron Gunnarsson's low shot was only inches wide.
At the other end Carl Cort's shot was deflected for the first corner of the game.
After doing most of the attacking, Norwich went behind after 19 minutes. Former Canary, David Bell, put in a low cross from the left and Henderson's shot beat Marshall low to his left.
Jason Shackell blocked a goalbound shot from Fox as the visitors took the game to Norwich.
As the game went into stoppage time Keiren Westwood was called into action for his first save of the afternoon when he held on to Shackell's goalbound header.
Before the half-time whistle Mark Fotheringham's low shot was also saved by Westwood.
The second half began with Jamie Cureton's shot being blocked. Jon Otsemobor then set up Cureton with the perfect cross only for Cureton to mis-kick on the six-yard line with the goal at his mercy.
However, the equaliser came after Westwood blocked Shackell's header from Sammy Clingan's left-wing corner and Grounds found the net from ten yards with a low left-foot drive.
Gunnarsson then set up Clinton Morrison, but he fired wide.
The officials missed a hand ball by Stephen Wright which should have earned Norwich a penalty.
The visitors weathered intense Norwich pressure and regained the lead in the 73rd minute, when Fox turned Carl Cort inside out before curling his left-foot shot into the net via Marshall's right-hand post.
Norwich had further penalty appeals turned down when Fotheringham's shot was blocked on the line and before the full-time whistle the home fans were streaming out of the ground, no doubt reconciled to the fact that they might be watching League One football next season.